Finite Product of Finite Sets is Finite
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Theorem
Let $\sequence {S_n}$ be a sequence of finite sets.
Let $\ds \prod_{k \mathop = 1}^n S_k$ be their Cartesian product.
Then $\ds \prod_{k \mathop = 1}^n S_k$ is also a finite set.
Proof
This theorem requires a proof. In particular: Boring induction from Product of Finite Sets is Finite You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 6$: Finite Sets: Corollary $6.8$